Jules Gilbert explains

[dsr at tao.merseine.nu]

> Unfortunately, without so much as a "hello", I was jumped on and
> declared to be a liar.

You may simply be deluded, instead.

> Continuing, so do the curve fit.  30 terms.
> 
> And from the resulting coefficients, produce an approximation of the 
> original input.

Bing! An approximation. NOT the original data. 

> In fact if you extract the left-most three or four significant bits you
> have yourself a very compressible signal.  Just remember that what does 
> not compress, you have to send.  And sending costs -- that's the measure
> by which all compressors are judged; how much do you have to send.

At this point, you cannot reconstruct the original data without
sending all of it.

> widely variant number's of columns.  But this is the gestalt of my
> learning:
> 
> Expect about 5k, maybe 7k compression per logical pass.  Not a lot, 
> I know.

But you can keep throwing away data forever! Well, until there
isn't any more. But you never get the original data back.

> And while this method doesn't have any merit, (because of the huge CPU
> overhead necessary to do the curve fitting,) other systems, not based 
> on floating point mechanics or involving integer DSP logic work well,
> Unfortunately, these are all bit based and, running on an X86 box, do
> require lot's of machine time.

I have discovered a wonderful method for infinite compression;
however, the margin of this book is too small to contain it.

Oh. Bad example. John Wilkes (is that his name?) eventually
solved Fermat's Last Conjecture. 

> Of course, this is a special case, because this process involves a step
> that requires lot's of CPU time!  As I keep saying, it's not practical. 
> But does it work?  Absolutely.

Not.

Stop deluding yourself: compress a nice executable file,
decompress it at the other end, and diff the original with your
output. Whoops.

-dsr-

-- 
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cause problems for the rest of the world, and so requires a little more
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